Novel method for the analysis of RLC circuits

The lagrangian formulation of classical mechanics is applied to RLC circuits. The generalized power function is introduced and the reduced Lagrange equations are used in the analysis of the system. This new method seems to be more useful than the conventional Kirchhoff taws and Lagrange equations. This is illustrated by an example.     

A modelling study on kefir grain biomass growth: Influence of various minerals

In this study, the effect of initial kefir grain concentration and various minerals (MgO, MgSO₄.7H₂O, ZnSO₄.7H₂O, CaSO₄.1/2H₂O and Fe₂O₃) on the propagation of kefir grains and the pH evolution of kefir were investigated. The activated kefir grains were inoculated into very low fat (0.1%) cows’ milk under constant temperature (25°C) and impeller speed (100 rpm) for a propagation time of 24 h. Several mathematical models proposed to predict the pH value and kefir grain biomass increase vs propagation time were evaluated by the experimental results for all mineral additions; the Richards equation was found to be the most appropriate one. After evaluation of the experimental data, the most influential mineral addition providing 46.3% increase in kefir grain biomass was found to be MgO with a concentration of 0.30 g Mg²⁺/L. At this optimal condition, a model was derived for the kefir grain biomass concentration representing pH dependence.